Debye-Einstein Model Research Articles

Study of thermal properties of TiCNO by Debye-Einstein model and Debye-Grüneisen model

The thermal properties of TiCNO are studied from the Debye-Einstein model based on the first-principle in combination with the special quasi-random structural model, meanwhile the derived result is compared with those obtained by the Debye-Grüneisen model. The present results show that Debye-Einstein model is excellent in predicting the thermal properties of multicomponent random structure materials due to consideration of the 3 n − 3 optical frequencies at the Γ point to represent the contributions of optic branches, although the Debye-Grüneisen models is also effective methods for predicting the thermal properties of multicomponent materials. The two methods show that when temperature rises, the thermal expansion coefficients of TiCNO first increase rapidly and then slowly, and Debye-Einstein predicts a stronger volume sensitivity to lower temperature due to the contribution of 3 n − 3 optic frequencies at Γ point. Although both models also predict a comparable temperature dependence of bulk modulus, the high temperature softening effect of TiCNO calculated by Debye-Einstein is gentler than that from Debye-Grüneisen, which demonstrates that the influence of optical branches cannot be negligible. With temperature increasing, the thermodynamic entropy predicted by both models increases due to the greater disorder degree of the system. Moreover, the thermodynamic entropy predicted by Debye-Einstein is larger owing to considering the optical frequencies at the Γ point. Due to the strong coupling between the acoustic and optical phonons lying in low frequency regime, both isobaric and isochoric heat capacities predicted by Debye-Einstein are larger than those predicted by Debye-Grüneisen at low temperatures. This work is a useful reference for predicting the thermal properties of multicomponent materials.

Study of thermal properties of TiCN by Debye Einstein model, Debye Grüneisen model and quasiharmonic approximation

Thermodynamic properties of ternary ceramic TiCN are studied by first-principles calculation combined with the Debye Einstein model, which considers the contribution of 3n−3 optical frequencies at the Γ point; Debye Grüneisen model, which treats optical frequencies as acoustic ones; and quasiharmonic approximation(QHA), which is the most prevalent method in prediction of phonon dispersion and thermal properties. No imaginary frequency shows that TiCN has dynamic stability, and negative formation energy indicates the thermodynamic stability. Particularly, TiCN has low thermal expansion coefficient, which rises quickly firstly and then gradually as temperature rises. The study of bulk modulus shows that TiCN possess excellent resistance to the volume thermal deformation. For temperature effects of thermal expansion coefficient, heat capacity and entropy, the obtained results show that Debye Einstein model are apparently closer to the QHA at low temperatures. Our present results provide guideline for exploration of thermal properties of multicomponent materials.

Crystalline-liquid duality of specific heat in halide perovskite semiconductor

Crystalline-liquid duality in specific heat is observed in lead-free bismuth halide perovskite A3Bi2×9 [A= FA, MA, Cs, and X = I, Br, Cl] semiconductor. All crystals exhibit unusual liquid-like behavior and show substantial deviation from the classical Dulong-Petit law at room temperature. This unusual liquid-like behavior of specific heat is attributed to the dynamic disorder and strong anharmonicity in the soft crystal lattice. The low-temperature specific heat was modeled using the combined Debye-Einstein model and obtained Einstein modes demonstrate strong anharmonic coupling of the low-energy optical modes with acoustic modes resulting in ultrasoft frequency dampening of acoustic phonons. The combination of strong acoustic−optical phonon coupling, soft elastic layered structure, and abundance of low-energy optical phonons results in anomalous thermodynamic specific heat duality in these bismuth-based phonon glass electron crystals. Our study is of fundamental interest in thermodynamics and will help to design novel thermoelectric materials.

Local atomic structure distortions in the Dion-Jacobson ferroelectric CsBiNb2O7

Despite recent interest in Bi-containing layered-perovskite ferroelectrics due to high ${T}_{c}$, their rational design is constrained by a poor understanding of local atomic structures. Here, we use neutron total scattering and first-principles theory to examine the local atomic structure in Dion-Jacobson layered-perovskite ferroelectric $\mathrm{CsBi}{\mathrm{Nb}}_{2}{\mathrm{O}}_{7}$. We show that the instantaneous short-range atomic structure can be described by a Debye-Einstein model that accommodates atomic motions due to acoustic and low-energy optic phonon modes. We determine structural distortions due to localized atomic dynamics with extremely high resolution. These are in addition to ground-state relative ionic displacements. The magnitude of dynamic variations in ionic positions points toward strong electron-phonon coupling in this material.

Crystal field and lattice disorder effects on the low-temperature thermodynamic properties of TmF3

The temperature dependence of the heat capacity Cp(T), (2–300 K), and the lattice parameters a(T), b(T), and c(T) (5–300 K) TmF3 were experimentally studied. Anomalies in the studied characteristics were identified due to the influence on the thermal properties of trifluoride of the crystal field, and at the lowest temperatures (2–10 K), of a possible glass-like contribution due to disorder in the crystal lattice. As a result of our analysis of the excess contribution to the heat capacity (Schottky contribution, CSch(T)), we proposed a simplified scheme based on 1-1-7-5 splitting of the ground state of the Tm3+ ion, and determined the splitting parameters. The influence of the crystal field is also manifested through anomalies in the thermal expansion of TmF3. The temperature dependences of the unit cell volume of thulium trifluoride, and its heat capacity, were analysed using the Debye-Einstein model, and the model parameters are determined.

Heat Capacity of Scandoborate NdSc-=SUB=-3-=/SUB=-(BO_3)-=SUB=-4-=/SUB=-

Single crystals of trigonal neodymium scandoborate NdSc3(BO_3)4 were grown by the group method from a solution-melt based on bismuth trimolybdate. The molar heat capacity C(T) was studied in the temperature range 2-300 K and magnetic fields up to 9 T. The experimental curve was approximated by the combined Debye-Einstein model. The lattice contribution was determined from ab-initio calculations. Schottky anomaly was observed in the low-temperature region C(T) with the applied magnetic field. Keywords: crystal growth, magnetoelectrics, heat capacity, Schottky anomaly.

Low-temperature anomalies of thermodynamic properties of lanthanum trifluoride LaF3 and (SrF2)0.5 (LaF3)0.5 multivalent solid solution

Temperature dependences of the heat capacity Cp(T) (2–300 K) and lattice parameter a(T) (5–300 K) of LaF3 and (SrF2)0.5(LaF3)0.5, in addition to the earlier studied SrF2, are experimentally investigated for the first time. The experimental dependences of Cp(T) and the unit cell volume V(T) of the studied fluorides are analysed using the Debye–Einstein model considering the influence of the disorder of their crystal structures. The parameters of the model are determined. An anomalous arrangement of the Cp(T) and V(T) curves of the solution with respect to the corresponding curves of the components is revealed. At low temperatures (T < 150 K), the values of Cp(T) and V(T) of the solution exceed the values calculated by the additivity rule. At higher temperatures (T > 150 K), deviations towards smaller values are observed. We have established that the disorder in solid-solution crystal structure is the common reason of anomalies revealed. It is found that at low temperatures, the cause of these anomalies is a decrease in the vibrational frequencies in the solid-solution metal sublattice upon the replacement of Sr with La, which has a large size and mass. Such a replacement leads to distortions of the original structure and an increase in its disorder. At elevated temperatures, the deviations are caused by an increase in the vibrational frequencies in the F- sublattice due to distortion of the crystal structure, as well as the increased influence of the anharmonicity of the disordered crystal lattice vibration.

Theoretical study of ThO2 by first principles calculations

In this paper, the thermodynamic, structural properties and vibrational spectrum of thorium dioxide have been studied using the Density Functional Perturbation Theory (DFPT) and Density Functional Theory (DFT) in the framework of first principles calculations. Quantum espresso software, which is an open source computing code, has been used in order to compute the kohn-Sham equations to obtain the minimum total energy of crystal. The vibrational spectrum of the thorium dioxide was examined along various symmetrical directions, and the results showed the dynamical stability of the crystal system. The quasi-harmonic Debye-Einstein model as implemented in GIBBS2 Code was used to calculate the thermodynamic properties of thorium dioxide at high temperatures and pressures. The simulation results showed that the Debye temperature of thorium dioxide decreased with increasing temperature at a constant pressure and increased with increasing pressure at a constant temperature. Increasing the Debye temperature indicated an increase in the crystal stiffness and the average sound velocity. It was observed that the volumetric thermal expansion coefficient and gruneisen parameter decreased exponentially with increasing pressure at a constant temperature, while increased with increasing temperature at a constant pressure, indicating an increase in heat transfer in the crystal lattice

Ab initio investigations on lattice dynamics and thermal characteristics of ThO2 using Debye–Einstein model

Ab initio investigations on lattice dynamics and thermal characteristics of ThO2 using Debye–Einstein model

Anomalous electronic properties in layered, disordered ZnVSb

New materials discovery is the driving force for progress in solid state physics and chemistry. Here we solve the crystal structure and comprehensively study physical properties of ZnVSb in the polycrystalline form. Synchrotron x-ray diffraction reveals that the compound attains a layered ZrSiS-type structure ($P4$/nmm, $a$ = 4.09021(2) \AA{}, $c$ = 6.42027(4) \AA{}). The unit cell is composed of a 2D vanadium network separated by Zn-Sb blocks that are slightly distorted from the ideal cubic arrangement. A considerable amount of vacancies were observed on the vanadium and antimony positions; the experimental composition is ${\mathrm{ZnV}}_{0.91}{\mathrm{Sb}}_{0.96}$. Low-temperature x-ray diffraction shows very subtle discontinuity in the lattice parameters around 175 K. Bonding V-V distance is below the critical separation of 2.97 \AA{} known from the literature, which allows for V-V orbital overlap and subsequent metallic conductivity. From ab initio calculations, we found that ZnVSb is a pseudogap material with an expected dominant vanadium contribution to the density of states at the Fermi level. The energy difference between the antiferromagnetic and nonordered magnetic configurations is rather small (0.34 eV/f.u.). X-ray photoelectron spectroscopy fully corroborates the results of the band structure calculations. Magnetic susceptibility uncovered that, in ZnVSb, itinerant charge carriers coexist with a small, localized magnetic moment of ca. 0.25 ${\ensuremath{\mu}}_{\mathrm{B}}$. The itinerant electrons arise from the ordered part of the vanadium lattice. Fractional localization, in turn, was attributed to V atoms neighboring vacancies, which hinder full V-V orbital overlap. Furthermore, the susceptibility and electrical resistivity showed a large hysteresis between 120 K and 160 K. The effect is not sensitive to magnetic fields up to 9 T. Curie-Weiss fitting revealed that the amount of itinerant charge carriers in ZnVSb drops with decreasing temperature below 160 K, which is accompanied by a concurrent rise in the localized magnetic moment. This observation together with the overall shape of the hysteresis in the resistivity allows for suggesting a plausible origin of the effect as a charge-transfer metal-insulator transition. Ab initio phonon calculations show the formation of a collective phonon mode at 2.8 THz (134 K). The experimental heat capacity reflected this feature by a boson peak with Einstein temperature of 116 K. Analysis of the heat capacity with both an ab initio perspective and Debye-Einstein model revealed a sizable anharmonic contribution to heat capacity, in line with disordered nature of the material. Further investigation of the electron and phonon properties for ZnVSb is likely to provide valuable insight into the relation between structural disorder and the physical properties of transition-metal-bearing compounds.

Теплоемкость скандобората NdSc-=SUB=-3-=/SUB=-(BO_3)-=SUB=-4-=/SUB=-

Single crystals of trigonal neodymium scandoborate NdSc3(BO3)4 were grown by the group method from a solution-melt based on bismuth trimolybdate. The molar heat capacity C(T) was studied in the temperature range 2-300 K and magnetic fields up to 9 T. The experimental curve was approximated by the combined Debye-Einstein model. The lattice contribution was determined from ab-initio calculations. Schottky anomaly was observed in the low-temperature region C(T) with the applied magnetic field.

Structural Disorder and Heat Capacity of a Solid Solution between Cadmium and Strontium Fluorides

The heat capacity Cp(T) of cadmium fluoride, strontium fluoride, and the Cd0.5Sr0.5F2 solid solution has been studied experimentally (2–300 K). We have detected deviations ΔCp(T) of the Cp(T) data from additivity. The low-temperature (2–50 K), positive deviations ΔCp(T) have been tentatively attributed to the effect of two-level systems associated with the glasslike character of the low-temperature thermal properties of the solution due to disorder in the Cd–Sr sublattice. The high-temperature (100–300 K), negative deviations ΔCp(T) are caused by the effect of anharmonicity of lattice vibrations, whose increasing role is also associated with the disordered arrangement of atoms in the crystal lattice upon formation of the solution. The Cp(T) data for the solution of the system studied have been analyzed in the Debye–Einstein model. We have determined model parameters: characteristic temperatures Θi and the fractions of different contributions, ai, to total thermal characteristics of the substances studied.

Ангармонизм колебаний решетки и тепловые свойства твердых растворов Сd-=SUB=-1-x-=/SUB=-Sr-=SUB=-x-=/SUB=-F-=SUB=-2-=/SUB=-

The temperature changes in the crystal lattice parameters a (T) of cadmium and strontium difluorides, as well as their mutual solid solutions Сd1-xSrxF2 (x = 0.23, 0.50), were studied experimentally at temperatures of 5-300 K. The temperature dependences of the unit cell volume of the fluorides studied were analyzed in the Debye-Einstein model . An increased effect of the anharmonism of lattice vibrations of solutions due to the disorder of the crystal structure on their thermal properties is established. The model parameters and characteristics of the anharmonic contribution are determined. Based on the data obtained, the concentration dependence of the thermal conductivity of Сd1-xSrxF2 solid solutions at T = 300 K was calculated in the Calaway model, compared with published experimental data. The possibility of assessing the thermal conductivity of single crystals of solid solutions of the studied system on the basis of data on the thermal properties of solution components obtained on powder samples is shown.

Low-temperature thermodynamic and magnetic properties of clathrate-like arsenide Eu7Cu44As23

Experimental investigation of heat capacity, CP, unit cell parameter, a, as well as the ESR absorption for a clathrate-like compound Eu7Cu44As23 has been performed in the temperature range of 2–300 K. The CP(T) function exhibits a sharp maximum at the temperature of ferromagnetic ordering, Tc ≈ 17 K, whereas the a(T) shows no anomaly at this temperature. This unusual behavior is governed by the clathrate-like structure of Eu7Cu44As23, where Eu2+ guest cations residing in oversized cavities of the host framework order ferromagnetically imposing no influence on the framework dynamics. The analysis of maximum of the Cp(T) function at 2–20 K allows determining the exchange integral, J, which is a characteristic of the magnetic interaction Eu2+ – Eu2+: J ≈ 0.27 K The analysis of the temperature dependencies of heat capacity, CP(T), and unit cell volume, V(T), in the frames of the Debye-Einstein model enabled determining characteristic temperatures of host and guest subsystems. Along with this, the contribution of two-level systems into thermodynamic properties of Eu7Cu44As23 was evaluated and related to the possibility of guest Eu2+ cations to occupy nonequivalent positions inside the cages of the host framework. The ESR of Eu2+ in Eu7Cu44As23 was studied at 5–300 K. The intensity of the ESR signal shows a sharp drop at low temperatures, which confirms the ferromagnetic character of the magnetic phase transition in Eu7Cu44As23. The experimental ESR spectrum was approximated by two Dyson lines, L1 and L2, which correspond to two g-factors: g1 = 2.081 ± 0,030 and g2 = 2,094 ± 0,016. The increase in L1 linewidth with temperature at 75–275 K is d(ΔH1)/dT = 0.027 G/K. These values of g-factors and d(ΔH1)/dT are derived the exchange integrals of the interaction of the Eu2+ local moment with conduction electrons J1* = 0.241 eV and J1** = 0.252 eV accordingly. For L2 J2* = 0.255 eV. Value J2** ≈ 0.26 eV is valid in 100–130 K interval only. The change of ΔH2(T) slope at higher temperatures may be due to crystal field effect.

Specific features of the lattice dynamics of CaxSr1-x F2 solid solutions

The temperature changes in the heat capacity Cp(T) and lattice parameters a(T) of solid solutions of CaxSr1-x F2 are experimentally studied at temperatures of 2–300 K for x = 0, 0.25, 0.5, 0.75 and 1. Deviations from the Kopp-Neumann rule (Vegard's rule) in the values of Cp(T) and a(T) for these solutions are identified.The experimental dependencies of Cp(T) and a(T) for end-member crystals and their solid solutions are analysed using the Debye-Einstein model, taking into account the effects of anharmonicity of lattice vibrations at elevated temperatures, and the parameters of this approximation are determined. An anomalous arrangement of the curves for Cp(T) and a(T) is revealed for these solutions, relative to the corresponding dependence for end-member crystals. Despite cationic substitution taking place during the formation of solid solutions of the system under study, restructuring of the crystal structure mainly affects the nature of the oscillations of the anion sublattice. Most affected by the anharmonicity are the Einstein modes, corresponding to the vibrations of the F− ions, and the coupled vibrations of two different fluorine sublattices.

Modeling of unusual lattice properties of superconducting PuCoIn5 based on ab initio calculation

The volume of PuCoIn5 unit cell differs by about 30% from the corresponding volume of PuCoGa5 – a superconductor with a record high critical temperature for this class of compounds (Tc ~ 18.5 K). Such a change in volume can significantly affect the degree of electronic correlations, which are believed to be responsible for the unusual properties of PuCoGa5 and similar compounds. In the present work, an ab initio calculation of the ground state energy of PuCoIn5 is performed for different values of the unit cell volume. Based on the obtained results supplemented by the energy of lattice vibrations calculated in the framework of the generalized Debye-Einstein model, the temperature dependences of thermal and elastic properties of PuCoIn5 have been simulated. The anharmonicity of lattice vibrations in PuCoIn5 and PuCoGa5 is discussed, and the effect of electronic correlations on the heat capacity of these two compounds is analyzed.

Debye–Einstein model and anomalies of heat capacity temperature dependences of solid solutions at low temperatures

An approach is proposed for analysing the deviations of the heat capacity Cp(T) of solid solutions from the Kopp–Neumann rule (KNR) ΔC(T) = Cp(T) − CKNR(T). Temperature dependences of the heat capacity Cp(T) of selected compositions of systems (InP)x (InAs)1−x and (GaAs)x (InAs)1−x at temperatures of 5–300 K are analysed in the Debye–Einstein approximation. It was established that in the case of substitution of atoms in the cation subsystem (Ga3+ ↔ In3+) with the same subsystem of anions (As3−), the positive values of ΔC(T) at T 100 K are the result of a decrease in the fraction of the Debye contribution without changing the upper limit of the oscillation frequency. In the case of substitution in the cation subsystem (P3− ↔ As3−) with the invariant cation subsystem (In3+) to the low-temperature positive contribution of the additional low-frequency Einstein mode, a positive part is added from the modified Debye mode having the characteristic temperature θD below the additive value θDKNR. The adequacy of this model is confirmed by Raman scattering data.

Ab-initio calculations of structural, phonon and thermal properties of $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ Al x Ga 1 - x As alloy

Structural, phonon and thermal properties of $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ alloy for different values of x (x $$=$$ 0.0, 0.25, 0.5, 0.75 and 1.0) have been investigated by quasiharmonic Debye–Einstein model and Quantum Espresso package. The correction of Vegard’s law for lattice constant has been examined and has a good agreement with other experimental and theoretical works. TO–LO splitting at gamma point, which is related to breaking of cubic symmetry, has been calculated by optical phonon mode calculation. It is found that by increasing the amount of Al in $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ alloy, specific heat at constant pressure and Debye temperature will be increased.

Structure‐Related Thermal Properties of Type‐VII Clathrates SrNi2P4 and BaNi2P4 at Low Temperature

Heat capacity CP(T) (2–300 K) and unit cell parameters a(T), b(T), and c(T) (5–300 K) of type‐VII clathrates SrNi2P4 and BaNi2P4 have been investigated experimentally. The studied compounds are prepared by a two‐stage ampoule synthesis. Diffuse maxima of CP(T) near 5 K along with anomalies in temperature dependencies of unit cell parameters below 10 K are observed and related to the influence of two‐level systems in guest‐atom substructures. Joint analysis of temperature dependencies of heat capacity and unit cell volume of both clathrates within the frames of the Debye–Einstein model allowed determining characteristic temperatures of the clathrate frameworks and guest atoms as well as parameters of the two‐level systems. The relationships of the obtained characteristics and the peculiarities of the crystal structures of SrNi2P4 and BaNi2P4 are discussed.

Thermodynamic properties of misfit cobaltite [Bi2-xCa2O4][CoO2]1.7

We synthetized a misfit structure cobaltite [Bi2-xCa2O4][CoO2]1.7 and studied its thermal behavior by simultaneous thermal analysis (STA), low temperature heat capacity measurement in physical property measurement system (PPMS), differential scanning calorimetry (DSC) to measure heat capacity and drop calorimetry to obtain the relative enthalpy increments. The oxygen non-stoichiometry determined by thermogravimetry (STA data combined with weight loss measurement of the material reduced in hydrogen atmosphere) was analyzed in terms of point defect model resulting in two independent reactions, oxygen release and cobalt disproportionation, described by the respective enthalpy and entropy changes. The applied model satisfactorily describes two regimes of oxygen release/incorporation associated with the respective Co valency changes Co4+/Co3+ and Co3+/Co2+. The temperature dependence of the molar heat capacity above room temperature was derived by simultaneous least squares method from DSC and enthalpy data considering the contribution due to oxygen release and deviation from ideal stoichiometry. The low temperature heat capacity was analyzed in terms of a combined Debye–Einstein model.